REVIEW 2 cited by
Random vectors in the isotropic position
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
abstract
Let $y$ be a random vector in \rn, satisfying $$ \Bbb E \, \tens{y} = id. $$ Let $M$ be a natural number and let $y_1 \etc y_M$ be independent copies of $y$. We prove that for some absolute constant $C$ $$ \enor{\frac{1}{M} \sum_i \tens{y_i} - id} \le C \cdot \frac{\sqrt{\log M}}{\sqrt{M}} \cdot \left ( \enor{y}^{\log M} \right )^{1/ \log M}, $$ provided that the last expression is smaller than 1. We apply this estimate to obtain a new proof of a result of Bourgain concerning the number of random points needed to bring a convex body into a nearly isotropic position.
Forward citations
Cited by 2 Pith papers
-
Quantum algorithm for estimating volumes of convex bodies
A quantum algorithm estimates the volume of an n-dimensional convex body within error epsilon using O-tilde(n^3 + n^2.5/epsilon) membership queries, the first quantum speedup for this task.
-
A Geometric Perspective on the Injective Norm of Sums of Random Tensors
New geometric proof establishes nearly optimal bounds on the ℓ_p injective norm of sums of random tensors for all p ≥ 2 and tensor order r.
Discussion (0). Continue with ORCID to comment.